Ray (geometry, $\{p+tv:t\ge 0\}$)

A half-line beginning at $p$ with a nonzero direction vector $v$. Removing the endpoint gives an open ray; allowing every real parameter gives the whole straight line.

A ray with its endpoint removed. In the Argand plane, fixing the argument of $z-z_0$ specifies an open ray because the argument of zero is undefined.